Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
200.1-a1
200.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{8} \)
$0.95048$
$(a), (5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.722205338$
$4.406960782$
1.125265195
\( \frac{237276}{625} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( 3\) , \( -3\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+3{x}-3$
200.1-a2
200.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{4} \cdot 5^{4} \)
$0.95048$
$(a), (5)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{2} \)
$0.361102669$
$17.62784313$
1.125265195
\( \frac{148176}{25} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -2\) , \( -2\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-2{x}-2$
200.1-a3
200.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$0.95048$
$(a), (5)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$0.180551334$
$35.25568626$
1.125265195
\( \frac{55296}{5} \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
${y}^2={x}^{3}-2{x}+1$
200.1-a4
200.1-a
$4$
$4$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
200.1
\( 2^{3} \cdot 5^{2} \)
\( 2^{8} \cdot 5^{2} \)
$0.95048$
$(a), (5)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$0.722205338$
$4.406960782$
1.125265195
\( \frac{132304644}{5} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -27\) , \( -67\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-27{x}-67$
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.